D0 and D1 Brane With $\kappa_-$ and $\kappa_+$ Extended Symmetry

TL;DR

This paper extends the $mbda$ symmetry of D0 and D1 branes into a larger symmetry by converting second class constraints into first class, providing new gauge fixings and insights into their phase space structure.

Contribution

It introduces an extended phase space framework that enlarges the $mbda$ symmetry of D-branes, transforming second class constraints into first class constraints.

Findings

Different gauge fixings yield various system presentations.

A 'unitary' gauge recovers the original $mbda$ symmetry.

For D1 branes with zero electric field, all constraints become first class.

Abstract

D0 brane (D-particle) and D1 brane actions possess first and second class constraints that result in local $\kappa$ symmetry. The $\kappa$ symmetry of the D-particle and the D1 brane is extended here into a larger symmetry ($\kappa_-$ and $\kappa_+$) in a larger phase space by turning second class constraints into first class. Different gauge fixings of these symmetries result in different presentations of these systems while a "unitary" gauge fixing of the new $ \kappa_+$ symmetry retrieves the original action with $\kappa_- = \kappa $ symmetry. For D1 brane our extended phase space makes all constraints into first class in the case of vanishing world sheet electric field (namely $(0, 1)$ string).